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The inelastic scattering of muons has been measured using positive muons of momentum 10 GeV/c incident upon a liquid-hydrogen target. We present values of the differential cross section and of the virtual photon-photon absorption cross section for |q| in the range 0.05 to 1.2 (GeV/c)2 and for equivalent photon laboratory energies of 0.6 to 6.5 GeV.
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Measurements of the differential cross section for the inelastic scattering of 12-GeV/c muons on protons are reported. These measurements cover a kinematic range of |q2| (the square of the four-momentum transferred from the lepton) up to 4.0 (GeV/c)2 and of muon energy losses (ν) up to 9.0 GeV. Only the scattered muon is observed in an optical spark-chamber apparatus. The data are compared with electron-proton inelastic scattering, and analyzed in terms of possible lepton form factors and anomalous interactions. μ−p inelastic scattering is found to exhibit the same mild |q2| behavior as does e−p inelastic scattering. No experimentally significant deviation from the predictions of muon-electron universality has been found. If the ratio of muon to electron inelastic cross sections is parametrized by the form (1.0+|q2|ΛD2)−2, we find with 97.7% confidence that ΛD>4.1 GeV/c. The muon-proton cross sections on the average are slightly smaller than the electron-proton cross sections. This observation is not experimentally significant because such a difference might be caused by systematic errors, but this observation is used to speculate as to the most fruitful direction for future experiments.
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High statistics data on the structure functions F 2 of the proton and the deutron measured with the same apparatus in deep inelastic muon scattering are used to study the ratio of structure functions of neutron and proton F 2 n / F 2 p and their difference F 2 p - F 2 n . Both measurements are consistent with predictions of the quark-parton model and of QCD.
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We present a new determination of the nonsinglet structure function ${\mathit{F}}_{2}^{\mathit{p}}$ - ${\mathit{F}}_{2}^{\mathit{n}}$ at ${\mathit{Q}}^{2}$=4 ${\mathrm{GeV}}^{2}$ using recently measured values of ${\mathit{F}}_{2}^{\mathit{d}}$ and ${\mathit{F}}_{2}^{\mathit{n}}$/${\mathit{F}}_{2}^{\mathit{p}}$. A new evaluation of the Gottfried sum is given, which remains below the simple quark-parton model value of 1/3.
Errors of F2(D) are the estimated total uncertainties and those on the ratio and difference are statistical only.
Values of the Gottfried Sum Rule integral (GS) defined as the integral between X(C=MIN) and X = 0.8 of (F2(P)-F2(N))DX/X.
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New results for the double spin asymmetry $A_1^{\rm p}$ and the proton longitudinal spin structure function $g_1^{\rm p}$ are presented. They were obtained by the COMPASS collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH$_3$ target. The data were collected in 2011 and complement those recorded in 2007 at 160\,GeV, in particular at lower values of $x$. They improve the statistical precision of $g_1^{\rm p}(x)$ by about a factor of two in the region $x\lesssim 0.02$. A next-to-leading order QCD fit to the $g_1$ world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, $\Delta \Sigma$ ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of $g_1^{\rm p}$. The uncertainty of $\Delta \Sigma$ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function $g_1^{\rm NS}(x,Q^2)$ yields as ratio of the axial and vector coupling constants $|g_{\rm A}/g_{\rm V}| = 1.22 \pm 0.05~({\rm stat.}) \pm 0.10~({\rm syst.})$, which validates the sum rule to an accuracy of about 9\%.
Values of $A_1^{\rm p}$ and $g_1^{\rm p}$ for the 2011 COMPASS data at 200 GeV in ($x$, $Q^2$) bins.
Values of $A_1^{\rm p}$ and $g_1^{\rm p}$ for the 2011 COMPASS data at 200 GeV in $x$ bins averaged over $Q^2$.
Values of $A_1^{\rm p}$ for the 2007 COMPASS data at 160 GeV in ($x$, $Q^2$) bins.
Measurements have been made of the inclusive scattering of 96, 147, and 219 GeV muons from hydrogen, and of 147 GeV muons from deuterium. Results are presented for the nucleon structure function F2(x,Q2) [≡νW2(x,Q2)] for 10<ν<200 GeV and 0.2<Q2<80 GeV2. The value of F2 rises with Q2 at small x, and falls with Q2 at large x, in agreement with the ideas of quantum chromodynamics. An average value of the ratio σLσT≡R=0.52±0.35 has been obtained for the region 0.003<x<0.10 and 0.4<Q2<30 GeV2. The values of F2 from this experiment have been combined with those from other charged-lepton scattering experiments to determine moments of the structure functions. The variation with Q2 of these moments is used to derive values for Λ, taking into account corrections up to second order in αs. The fit to the data is very good.
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Results on the protron structure function, F2, are presented for 0.3<q2<80.0 GeV2 and 10<ν<200 GeV. The results support the conclusions of earlier work at 97 and 147 GeV that scaling is violated. A new value for R=σSσT=0.44±0.25 has been obtained using all the Fermilab proton measurements.
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We have measured muon-proton deep inelastic scattering in the range 0.4<q2<3.6 (GeV/c)2. The data are consistent with muon-electron universality, and if the ratio ρ=νW2(μ−p)νW2(e−p) is fitted with the form ρ=N(1+q2Λ2)−2, we obtain N=0.997±0.043 and Λ−2=+0.006±0.016 (GeV/c)2. This result establishes that |Λ|>~5.1 GeV/c with 95% confidence.
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Experimental results obtained at the CERN Super Proton Synchrotron on the structure-function ratio F2n/F2p in the kinematic range 0.004<x<0.8 and 0.4<Q2<190 GeV2, together with the structure function F2d determined from a fit to published data, are used to derive the difference F2p(x)-F2n(x). The value of the Gottfried sum F(F2p-F2n)dx/x=0.240±0.016 is below the quark-parton-model expectation of 1/3.
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The ratio of the deuteron to proton structure functions is measured at very small Bjorken x (down to 10–6) and for Q2>0.001 GeV2 from scattering of 470 GeV muons on liquid hydrogen and deuterium targets. The ratio F2n/F2p extracted from these measurements is found to be constant, at a value of 0.935±0.008±0.034, for x<0.01. This result suggests the presence of nuclear shadowing effects in the deuteron. The dependence of the ratio on Q2 is also examined; no significant variation is found.
F2(N) / F2(P) = 2F2(DEUT)/F2(P) - 1.
F2(N) / F2(P) = 2F2(DEUT)/F2(P) - 1. The systematic uncertainty in the Q**2 dependece is negligible as compared to the statistical uncertainty.
The proton and deuteron structure functions F2p and F2d are measured in inelastic muon scattering with an average beam energy of 470 GeV. The data were taken at Fermilab experiment E665 during 1991 and 1992 using liquid hydrogen and deuterium targets. The F2 measurements are reported in the range 0.0008<x<0.6 and 0.2<Q2<75 GeV2. These are the first precise measurements of F2 in the low x and Q2 range of the data. In the high x range of the data where they overlap in x and Q2 with the measurements from NMC, the two measurements are in agreement. The E665 data also overlap in x with the DESY HERA data, and there is a smooth connection in Q2 between the two data sets. At high Q2 the E665 measurements are consistent with QCD-evolved leading twist structure function models. The data are qualitatively described by structure function models incorporating the hadronic nature of the photon at low Q2. The Q2 and the W dependence of the data measure the transition in the nature of the photon between a pointlike probe at high Q2 and a hadronic object at low Q2.
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We present results on the cross-section ratio for inelastic muon scattering on neutrons and protons as a function of Bjorken chi;. The data extend to χ values two orders of magnitude smaller than in previous measurements, down to 2×10 −5 , for Q 2 >0.01 GeV 2 . The ratio is consistent with unity throughout this new range.
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The structure functions F p 2 and F d 2 measured by deep inelastic muon scattering at incident energies of 90 and 280 GeV are presented. These measurements cover a large kinematic range, 0.006⩽ x ⩽0.6 and 0.5⩽ Q 2 ⩽55GeV 2 , and include the first precise data at small x , where large scaling violations are observed. The data agree with earlier results from SLAC and BCDMS but exhibit differences with respect to those of EMC-NA2. Extrapolations to small x of recent phenomenological parton distributions are shown to disagree with the present results.
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The spin asymmetry in deep inelastic scattering of longitudinally polarised muons by longitudinally polarised protons has been measured over a large x range (0.01< x <0.7). The spin-dependent structure function g 1 ( x ) for the proton has been determined and its integral over x found to be 0.114±0.012±0.026, in disagreement with the Ellis-Jaffe sum rule. Assuming the validity of the Bjorken sum rule, this result implies a significant negative value for the integral of g 1 for the neutron. These values for the integrals of g 1 lead to the conclusion that the total quark spin constitutes a rather small fraction of the spin of the nucleon.
THE AVERAGE VALUES OF Q**2 IN EACH X-BIN ARE AS FOLLOWS: X=0.015,Q2=3.5: X=0.025,Q2=4.5: X=0.035,Q2=6.0: X=0.050,Q2=8.0: X=0.078,Q2=10.3: X=0.124,Q2=12.9: X=0.175,Q2=15.2: X=0.248,Q2=18.0: X=0.344,Q2=22.5: X=0.466,Q2=29.5.
SMC is progressing a series of experiments to reveal the spin structure of nucleon at CERN. The first experiment on deuteron has been performed in 1992. We will report here the data on deuteron and discuss the present status of nucleon spin structure using all data including SMC and also E142(SLAC) data recently reported.
First moment of the spin-dependent structure function G1.
The spin-dependent structure function g 1 p has been measured by deep inelastic scattering of polarized muons off polarized protons at 190 GeV incident muon energy. The data cover a kinematic range of 1 < Q 2 < 80 GeV 2 and 0.003 < x < 0.6, where −Q 2 is the squared 4-momentum transfer and x is the Biorken scaling variable. The first moment Γ 1 p = ∫ 0 1 g 1 p d x = 0.152 ± 0.015( stat. ) ± 0.018( syst. ) is smaller than the prediction of the Ellis-Jaffe sum rule by one standard deviation. This result leads to a contribution of the quark spins to the proton spin of δΣ = 0.36 ± 0.21. All results presented here are preliminary.
First moment of the spin-dependent structure function G1.
The ratio of the structure function F 2 n / F 2 p ( x ) has been measured in deep inelastic scattering of 274 GeV muons on hydrogen and deuterium targets exposed simultaneously to the beam. The results were obtained from 0.3 (0.6) million events from hydrogen (deuterium) in the range 0.004 < x < 0.8 and 1 < Q 2 < 190 GeV 2 . At x < 0.25 both the statistical and the systematic error is below 2%. Implications for parton distributions and for the σ w / σ z production cross section ratio in p p collisions are discussed. When compared to other results obtained at lower energies, the data indicate a Q 2 dependence of the ratio.
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Results are presented on the ratio of neutron and proton structure functions, F 2 n / F 2 p , deduced from deep inelastic scattering of muon from hydrogen and deuterium. The data, which were obtained at the CERN muon beam at 90 and 280 GeV incident energy, cover the kinematic range x = 0.002−0.80 and Q 2 = 0.1−190 GeV 2 . The measured structure function ratios have small statistical and systematic errors, particularly at small and intermediate x . The observed Q 2 dependence in the range x = 0.1−0.4 is stronger than predicted by perturbative QCD. From the present data together with results from other experiments it is suggested that the twist-four coefficient for the proton is smaller than that for the neutron for x larger than 0.2.
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Merged 90 and 280 GeV data.
Results are presented for F2d/F2p and Rd-Rp from simultaneous measurements of deep inelastic muon scattering on hydrogen and deuterium targets, at 90, 120, 200 and 280 GeV. The difference Rd-Rp, determined in the range 0.002<x<0.4 at an average Q^2 of 5 GeV^2, is compatible with zero. The x and Q^2 dependence of F2d/F2p was measured in the kinematic range 0.001<x<0.8 and 0.1<Q^2<145 GeV^2 with small statistical and systematic errors. For x>0.1 the ratio decreases with Q^2.
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The proton structure function F 2 has been measured in the range 2.5 ⪕ Q 2 ⪕ 170 GeV 2 and 0.03 ⪕ x ⪕ 0.65 . Scaling violation is clearly seen in the data. Results of fits to leading-order QCD are presented, together with values of the scale-breaking parameter λ.
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Results are presented on the difference in R , the ratio of longitudinally to transversely polarised virtual photon absorption cross sections, for the deuteron and the proton. They are obtained by comparing the ratio of cross sections for the deep inelastic scattering of muons from deuterium and hydrogen targets at 90 and 280 GeV incident energy. The results cover the range x =0.01–0.30, at an average Q 2 of 9 GeV 2 . The measured difference R d - R p shows no significant x dependence and is compatible with zero, as well as with expectations from perturbative QCD. We use the same method to obtain the difference R Ca - R C from cross section ratios measured on carbon and calcium targets at 90 and 200 GeV incident energy.
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Average overall x values.
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We present results on a high statistics study of the proton structure functions F 2 ( x , Q 2 ) and R = σ L / σ T measured in deep inelastic scattering of muons on a hydrogen target. The analysis is based on 1.8 × 10 6 events after all cuts, recorded at beam energies of 100, 120, 200 and 280 GeV and covering a kinematic range 0.06 ⩽ x ⩽ 0.80 and 7 GeV 2 ⩽ Q 2 ⩽260 GeV 2 . At small x , we find R to be different from zero in agreement with predictions of perturbative QCD.
THE AVERAGE VALUES OF Q**2 AT EACH OF THE X VALUES LISTED IN THIS TABLE ARE 15,20,20,25,30,35,40,45,50,50.
R=SIG(L)/SIG(T) IS TAKEN TO BE ZERO.
R=SIG(L)/SIG(T) IS TAKEN TO BE ZERO.
The energy distribution of inclusive hadrons produced by 280 GeV muons on hydrogen and deuterium targets are compared. The sum of the scaled energy distributions of the positive and negative hadrons is found to be the same for the two targets. The difference of these distributions is observed to factorise inx andz and thez-dependence is found to be independent of the target type and have a form (1−z)2.1±0.2. The net charge of the hadronic jet is positive at highx even in the case when the scattering takes place on the neutron. These results are in good agreement with the expectations of the Quark Parton Model.
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We measured the spin asymmetry in the scattering of 100 GeV longitudinally-polarized muons on transversely polarized protons. The asymmetry was found to be compatible with zero in the kinematic range $0.006<x<0.6$, $1<Q~2<30\,\mbox{GeV}~2$. {}From this result we derive the upper limits for the virtual photon--proton asymmetry $A_2$, and for the spin structure function $g_2$. For $x<0.15$, $A_2$ is significantly smaller than its positivity limit $\sqrt{R}$.
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Nucleon spin structure function g2.